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基于交叉降阶取样的改进响应面方法
An improved response surface method based on cross order reduction sampling
投稿时间:2021-12-30  修订日期:2022-01-13
DOI:
中文关键词:  交叉降阶  响应面法  结构可靠度  可靠度指标  样本点
英文关键词:cross order reduction method  response surface method  structural reliability  reliability index  sampling point
基金项目:
作者单位邮编
夏雨 广西科技大学 545006
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中文摘要:
      针对经典响应面法计算精度不高和稳定性不强的问题,提出了交叉降阶的思想,并基于此发展出一种新的改进响应面方法。首先,改进初始点选取,而后在选点过程中,引入星型设计法,将n维坐标系分割成n-1个不含抽样中心点的一维坐标系和1个既含有抽样中心点又有试验点的一维坐标系。在前n-1个坐标系中,考虑样本点和极限状态面之间的距离以筛选样本点;而在最后一个坐标系中,在正向试验点和抽样中心点中交叉选点,然后用选取的样本点去拟合线性模型。最后通过五个数值算例与工程算例,验证了交叉降阶响应面法具有较高的精度、效率和稳定性。
英文摘要:
      In order to solve the problem that the calculation accuracy and the stability of the classical response surface method is not high in some cases, an improved response surface method based on the cross order reduction method for structural reliability analysis was proposed. First of all, the way of the selection of initial point was improved, Secongly, in the process of selecting sampling points, the star design method was introduced in this paper, and the n-dimensional coordinate system was divided into n-1 one-dimensional coordinate systems without sampling center points and one one-dimensional coordinate system with both sampling center points and experiment points. In the former n-1 coordinate systems, the distance between the sampling points and the actual limit state surface was considered to select the sampling point, while in the last coordinate system, a better point was selected between the positive experiment point and the sampling center point, and then the selected n sample points were used to fit the linear response surface function until the convergence condition was met. Finally, the feasibility of the proposed method is verified by comparing with traditional response surface method and weighted regression method, and the rusults are presented to demonstrate that the proposed method guarantees higher accuracy and can ensure its computational efficiency and stability.
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